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Math Help - Two questions about vectors and scalars?

  1. #1
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    Two questions about vectors and scalars?

    Is vector A divided by magnitude of a, is a scalar or a vector. I think it is a vector because the direction is not eliminated.

    My other question is, using vectors explain why |a+b| is always less than |a|+|b|.
    I think it is always smaller than |a|+|b| because it goes in a straight line, from point a to point c, and not a-to-b-to-c. For example, |a+b| of the 3,4,5 triangle is 5, while |a|+|b| is 7. This means you will have a less magnitude because you will be going in a straight line.
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  2. #2
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    Quote Originally Posted by Barthayn View Post
    Is vector A divided by magnitude of a, is a scalar or a vector. I think it is a vector because the direction is not eliminated.
    Yes. (Is it significant that you used an uppercase and a lowercase a?) The magnitude of a vector is a scalar, and a vector multiplied or divided by a scalar is a vector.

    My other question is, using vectors explain why |a+b| is always less than |a|+|b|.
    I think it is always smaller than |a|+|b| because it goes in a straight line, from point a to point c, and not a-to-b-to-c. For example, |a+b| of the 3,4,5 triangle is 5, while |a|+|b| is 7. This means you will have a less magnitude because you will be going in a straight line.
    This is called the triangle inequality.
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  3. #3
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    Hello, Barthayn!

    \text{Is vector }\vec a\text{ divided by magnitude of }\vec a\text{ a scalar or a vector?}

    \text{I think it is a vector because the direction is not eliminated.}

    You are correct!


    In fact, this has a special name.

    . . \dfrac{\vec v}{|\vec v|}\,\text{ is the }unit\:vector\text{ in the direction of }\vec v.

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